Electrical filter circuits



June 2l, 1960 w. c. DEAN 2,942,195

ELECTRICAL FILTER CIRCUITS Filed May 15, 1958 a 7x 8x 9 5 1! 2 NTU-4+@,10

4 Sheets-Sheet 1 El? 3 @o 4/ 45 I INVENTOR.

47 5 wa/4M cau/v 3^- 1, BY

June 21, 1960 w. c. DEAN 2,942,195

ELECTRICAL FILTER CIRCUITS Filed May 15, 1958 4 Sheets-Sheet 2 INVENTQR.#WM/4M C 054A/ June 2l, 1960 w. c. DEAN 2,942,195

ELECTRICAL. FILTER CIRCUITS Filed May 15, 1958 4 Sheets-Sheet 3 0 4INVENTOR. Y W/ MM C 054A/ June 21,'*1960 w. c. DEAN 2,942,195

ELECTRICAL FILTER CIRCUITS Filed May l5, 1958 4 Sheets-Sheet 4 United yStates Patent O 2,942,195 ELECTRICALFVILTER CIRCUITS William C. Dean,Indiana Township, Allegheny County,

Pa., assigner to Gulf Research 8c Development Coinpany, Pittsburgh, Pa.,a 'corporationlof Delaware Filed May 1-5, 195s, ser. No. 135,458

6 Claims. (c i. 328-138) This invention relates to electrical filtercircuits and in particular relates to a iilter circuit comprising anelectrical network system whose response to an impulse may be made tohave any desired `impulse response and which network is amenable tocomputation and whose/physical parameters may be accomplished withaccuracy. The filter system of this invention is particularlyadvantageous in the determination of optimum characteristics required ofa seismograph when` the seismograph is required to elect maximumsignal-to-noise ratio.

In reflection seismograph prospecting operations it has vbeen customaryto electrically eiect certain changes in the seismograph signal in orderto increase the ratio of reliected seismic signal to noise. Commondevices for doing this are, for example, band-pass lter circuits havinga known steady-state frequency response characteristie and the purposeof these ilters is to attenuate the predominating noise frequencies ascompared to the frequencies of the useful seismic signal. However,seismic impulses are transient in character and it is often advantageousto examine the transient response characteristic of seismograph filters.Such an analysis is herein termed ftime-dornain filtering and thefilters are herein termed time-domain ilters.

It is possible with time-domain filters to obtain lter characteristicsthat are not attainable with conventional Vband-pass iilters. Forexample, time-domain iilters can be made to perform integrations,differentiations, or have The signal-to-noise ratio may be well-knownstep function. The present invention relates,

"to time-domain filters of this generaltype.

Time-domain filters have heretofore been approximated by means oftime-delay iilters and the latter have been v-employed .in the analysisof seismograms. Such timeydelay filters employ multiple magneticreproducing heads to play back a magnetically-recorded seismogram withadjustable delay times, the reproductions being .combined A'in variousways. This system, however, is very expensive :and cumbersome because ofthe many reproducing heads required. Furthermore it is susceptible toerror in that the delay times must be small and are diflicult to physi--tcally set up with accuracy. Furthermore the high frequency response ofsuch a system cannot be specified beyond some given nite frequency.

One of the difficulties of constructing electrical filters lies in thediiiiculty of computing desirable or required vcharacteristics which areprescribed by the particular type of signal and noise encountered in anyparticular seismic operation. A highly `desirable sesismic filter is onewhose characteristics are readily adjusted in such manner that52,942,195 Patented June 21, 1960' the response is amenable tocomputation and which at the same time can readily be set up in aphyiscal form closely` approximating that required by the computationswhich are usually based on the use of ideal components; By an idealcomponent is meant an inductance without resistance or other losses, acapacity without losses, `and a resistor without distributed capacity orinductance.

One way in which time-domain filters may be set up is disclosed in U.S.Patents Nos. 2,024,900; 2,124,599; and 2,128,257 to Wiener and Lee.These patents teach the use of an extended electrical network of arepetitive character called a symmetrical lattice network.` Thesepatents also teach sampling the signal at corresponding points along thelattice network, i.e. after the signal has traversed various numbers oflattice sections. The various signal samples are then adjusted todesired amplitude and polarity and combined in order to produce anoutput. By this means it is possible to obtain a filter whose outputapproximates` any desired transient response by merely adjusting thepolarity and amplitude of the signal samples that are combined. Aserious diiculty arises in physically settingup any extended latticenetwork of the type disclosed in the above-mentioned patents in that thetheory'disclosed in the patents requires the use of ideal inductancesAand coridensers. Such networks are diiicult to set up and if physicalcomponents are used that include losses, either ,the `exact theoreticalcomputations become cumbersome and inaccurate, or the actual behavior oithe physical system poorly approximates the desired computed behavior. Afurther diiculty arisestwith the lattice networks` of theabove-mentioned patents in that most of the lattice sections are aboveground potential giving rise to distributed-capacityeffects, leakage toground, and instability that is undesirable.

This invention provides electrical networks of th ladder type (ascontrasted to lattice-type network) and combines the ladder with othercomponents in such manner that the transient response resulting from a`combined sampling at successive points of the ladder network as well asat the other components is readily computable with precision. The ladderand other networks employed in this invention have the furthercharacteristic that the components need not be ideal, so that losses inthe inductances and losses in the condensers do not seriously aiect theresult. Furthermore the circuits of this invention have the physicallyhighly-desirable Acharacteristic that one side of the network may employa running ground which materially enhances stability, convenience ofconstruction, reduces the number of components required andsubstantially reduces the eiiects of distributed capacity `to ground.

' Reference will be made to the drawings forming a part of thisspecification and in which:

Figure l shows a generalized block diagram of the circuit described inthe prior art and which employs `a symmetrical lattice networkillustrated in Figure 1(a);

Figure 2 shows a generalized block diagram of the circuits of thisinvention Vand which employ a ladder `network illustrated in Figure2(a);

Figure 3 shows a graph of a typical impulse type of input signal; Y i

Figure 4 shows a graph of `a typical transient response which may beexpected from the circuit oi Figure 2 as a result of an input impulsesimilar to that of Figure 3;

Figure 5 shows a wiring diagram of a circuit element whose operation ishelpful in understanding the invention;

Figures 6, 7, 8, 9, 10, and 1l show detailed wiring `diagram-s ofnetworks employed in this invention; q i Figures l2 and 13 show detailedwiring diagrams of sampling circuits which may be employed in thisinvention;

Figures 14 and 15 show detailed wiring diagrams of summing circuitswhich may be employedl in this invention;

FigureV 16 shows a detailed wiring diagram of an integrator employed inthe network of Figure l1; and v Y Figure 17 shows a detailed wiringdiagram of an ampliiier employed in the network of Figures 9, l0, and11.

Referring to Figure 1 there is indicated an extended `lattice networkwhose respective sections are indicated by 1, 2, 3, etc. 4. Therespective sections are connected in succession as shown with the inputto section 1 applied at terminals 5. Section 1 delivers its output tosection 42 at terminals 6. Section 2 delivers its output to section 3yat terminals 7, and so on. It is understood that between the Isections3 and 4 of Figure l there may be interposed many similar sections. Theoutput of the last section 4 is connected -to Van appropriateterminating resistor 10. In the aforementioned Patent 2,024,900 such anetwork is employed and 'the signal is sampled at points 6, 7, 8, etc.'9, and these samples are combined to form the output ofthe system whichis delivered at terminals 16. The signal obtained from terminals 6, 7,8, etc. 9 are adjusted as `to polarity and amplitude by means ofsampling circuits 12, 13, 14, etc. v whose outputs are algebraicallypombined by a summing circuit 11 whose output is delive'red to theoutput terminals 16. In the above-men- J,tioiied prior-art patents thenetworks forming the sections f1, 2, 3, etc. 4 lare symmetrical latticesections, a lattice Abeing characterized v-by having a shunt impedancewhich bridges a Vseries 4impedance of the same section. In thesymmetrical lattice sections disclosed in said Patent 2,024,900 theseries impedances Z1 are equal as shown in Figure 1(a), and the shuntimpedances Z2 are-also 'equal as shown in Figure l(a). There are nogrounds 'on the respective lattice sections as the presence of more:than one ground would obviously very materially change the circuitrelationships. This results in the aforementioned diiiiculties whichbecome particularly troublesome 'when one attempts to apply the systemdisclosed in the prior art to low-frequency operation such as isencountered in seismic prospecting operations.

.The present invention employs a ladder network 'in Vcombination with atleast one auxiliary network of the proper form. l A typical ladderysection employed in Vthis invention vis illustrated in Figure Zta). Inthe invention theoutputs from'the respective Ysections of thel ladder aswell as the output from the auxiliary network are sam- Vpled andcombined to form the system output. The in- V veritionV provides'specific'combinations of particular types -of ladder Vnetworks with aparticular auxiliary network. vIn "some Vembodiments the auxiliarynetwork precedes theladder, and in some embodiments Vthe auxiliarynetwork follows the ladder. All embodiments of the invention arecharacterized in that the particular ladder network used may havea'running, ground whereby the various elements of the laddersections arealways operated l'at the lowest practical potential above ground, thusminimizing the eifects of distributed capacity in the'ladder elements.'In Vthose embodiments which employ induct- V-a'nces substantially allof the inductances may be resistive, ile. the inductances haveseries-connected resistors which may take into account therlosscomponent of Ythe coilsemployed as inductances The preferred embodimentemploys only resistors and condensers and completely avoids the use ofinductances.

Figure 2 illustrates in block diagram form the schematic wiring of thisinvention. The ladder network, one section of which is illustrated inFigure 2(a), Vcomprises sections 21, 22, 23, etc. `24 which-must be of a4particular type to be specifically described later. In lthe laddersectio'n shown in Figure 2(a) the impedancesZg are equal and suchV asectionis commonly4 termed 'a 1r section. Auxiliary 'network 25(0) or25(12), vwhich must also be of particular type to be described, isconnected either preceding the ladder network as is 'for example 2501),or connected following the ladder network as is for example 25 (b). Thevoltage at the section junctions 26, 27, 28, etc. 29 are sampled andVadjustedasntdknown polarity and rmagnitude by the calibrated samplingcircuits 32, 33, 34, etc.35. V.If a preceding `auxiliary network 25,(a)isv employed then the voltage at its output 30(a) is also sampled andthis sample is adjusted as 'to known polarity and magnitude by `means ofsamplingY network -36(a), 'and if a following Y Y auxiliary network2`5(b) is employed then the Vvoltageat its output 30('b) is sampled andthis sample is adjusted as to known polarity and magnitude bythesampling network 36(b). A terminating resistor 38 is connected tothelast'section"whether'itf'bethe'dast ladder section or the end of thefollowing auxiliary network. By employing one .of the particularnetworks 2501) or 2.5(b) herein described in combination with one of theparticulai ladder networks 21, 22, 23, etc. 24 herein described,` it ispossible to operate with a ground on one ,side-'of the system, i.e. atone. of the input terminals 39 and one of the terminals 26, 27, 28, etc.29, 3001) or V'30*(b.) as shown by the ground connection 31. The groundconnection 31 also grounds one input terminal of each sampling circuit32,33,- 34, etc. 35, Vand 36(a) or 36(1)). The outputs of lthe samplingcircuits 32, 33, 34, etc. 375, and 36(a) or 36(b) are algebraicallyVcombined by the summing circuit 37 whose output is delivered toterminals 40.l The circuits 32-36 are known and willtbe describedbriefly later. They are all calibrated ,so -that their respectiveadjustments may be read olf their respective dial settings.

It is convenient to consider the response at terminals 40 of the circuitof Figure 2 when a standard type of -input is applied to the inputterminals 39. One such type of input is thewell-known step function inwhich the input voltage (e) is zero until time z=0 and thereaftere=constant, usually made unity. However, for purposes of the presentinvention it is preferred to em- `ploy an impulse type of voltage inputsuch as shown in Figure3. Whenever an impulse of the type illustrated inFigure 3 is applied to the input of the circuit of Figure ,2 it will'produce a decaying transient output. Figure V3 'shows Va plot of theinput voltage applied to terminals 39 of 'Figure 2. The voltage is Zerountil the time Zero, whereupon Vthe Voltage suddenly attainsV a value(e1) 'indicated at '17 for a very short instant of time (At), and thenfalls suddenlyagain to Zero as indicated by the dropi-,t'Suglnanalnalsslne `the forrn'of'a'Diracfdelta' function and isdefined by the expression limit At-soternttei Y This impulse-*or DiracdeltaV function type ofrinput `is V:readily amenable to computation foranalytically com- :puting the transient response of a system such'asillustrated Vin Figure 2. The impulse may readily be generatedphysically byV means of a contactor which momenexpectedat theoutpntterminals 40 of a circuit such as that of Figure 2 when an impulsesuch as that of Figure 3 is applied at its input terminals 39. The (e0)voltage at the output-terminals 40 is zero until z=0 whereupon theVoutput voltage executes a transient-response curve illustrated by 20 inFigure 4. After a certain length of time the output voltage of courseagain becomes zero. rlfhe character Vof, the Acurve 20V -w-ill depend onthe nature of' theel'eme'nts 21),' 22,V 2,3, `etc. 24 and '25(01)or'25(`b'),

and on the respective adjustments of sampling circuits 32,33, 34, etc.35, and 3601) or 36(b). The curve 20 is termed the impulse response ofthe network. If a circuit having the impulse-response curve 20 shown =inFigure 4 is employed as a seismograph filter, then it is apparent thatthe character of curve 20 will profoundly alfect the type of seismogramobtained when using this particular circuit in the seismograph channel.Those skilled in the seismograph `art will recognize that wave trainssimilar to that shown in Figure 4 are often seen on reflectionseismograms when made with the use of filters. In the case of thecircuit of Figure 2, the nature Iof the curve 20 may be varied byvarying the adjust- :ment of the sampling circuits 32, 33, 34, etc. 35,and 36(51) or`36(b).

It is impractical to attempt to adjust in the field all of the samplingcircuits 32, 33, 34, etc. 35, and 36(a) or 36(b) shown in Figure 2. Thenetwork of Figure 2 is also physically too heavy and complex for routinefield operations. However, it is relatively simple to record the seismicimpulses in the field `with high fidelity so that the resultingseismogram will contain all of the seismic impulses and all of theassociated noise. 'Ihe field seismogram is made in aphonographically-reproducible form, for example on magnetic tape or inthe form shown in Rieber Patent No. 2,051,153, so that it maysubsequently be played back in the laboratory as often as desired. Theplay-back means may then include an adjustable filter of the type shownin Figure 2 and the effect of various filter adjustments may then beobserved -in the laboratory. By observing the output voltage on acathode-ray oscilloscope during repeated reproduction of the seismogram,the operator can adjust the sampling circuits 32, 33, 34, etc. 35, and36(a) or 36(b) to obtain the best possible reflection-to-noise ratio.The sampling circuits 32, 33, 34, etc. 35, and 3601) or 36(b) are eachcalibrated beforehand so that the polarity and magnitude of the samplesdelivered by them at optimum adjustment will be known. Having thusdetermined the optimum adjustments for the sampling circuits 3236, itbecomes possible to compute an equivalent simpler filter circuit i.e.one which is less complex than that of Figure 2. This simple circuitwill reproduce the characteristics which pertain to Figure 2 withoptimum adjustment. A check on the solution can be made by com-paringthe impulse response curve of the computed filter with that of Figure 2in optimum adjustment. Such 4a simple iilter circuit may thereafter beemployed in tield operations in the area for which the originalseismogram was typical, with the assurance that it will produceseismograms having optimum reiiection-to-noise ratio for this area. Eachtypical area may be simil-arly investigated and the optimum filter forsuch area determined.

It is known that an impulse response of the character shown by curve 2l)of Figure 4 may be represented by the sum of a series of functions knownas Laguerre functions. This may be written as e0=2anln(l) in rwhich anis a coeiiicient that may be either plus` or minus, and l(t) is theLaguerre function of degree n. Various forms of Laguerre functions havebeen computed by mathematicians and engineers and their values areknown.

See for instance Y. W. Lee, Synthesis of Electrical Networks by Means ofthe Fourier Transforms of Laguerres Functions, Massachusetts Instituteof Technology Thesis, 1930, also published in Jour. Math. Phys., vol.II, pp. 83-113, June 1932; P. R. Aigrain and E. M. Williams, Design ofOptimum Transient Response Amplifiers, Proc. I.R.E., vol. 37, pp.873-879, August 1949;

D. Jackson, Fourier Series and Orthogonal Polynomi-' nais, CarusMonograph No. 6, The Math. Assn. of America, Oberlin, Ohio, 1941; G.Szego, Orthogonal Polynominals, Am. Math. Soc. Coll; Pub., vol. 23,

v21.939; E. E. Ward, The Calculation of Transents in Dynamical Systems,Proc. Cambridge Phil. Soc., vol. 50, part I, pp. 49-59, January 1954.)

` In this invention the network elements 21, 22, 23, etc. 24, and 25(61)or 25(b) are of such form that the impulse responses at the respectivepoints 3001), 26, 27, 28, etc. 29, 30(b) are given by members of aseries of Laguerre functions. In this invention only theseries ofLaguerre functions of the form c tLnUct), where Ln(kt) is a Laguerrepolynominal of degree n and e is the base of natural logarithme and k iseither 1 or 2, will be considered. In certain embodiments of theinvention k=l and in other embodiments lc=2 as will be indicated. Bymaking the elements 21, 22, 23, etc. 24, and 25(a) or 25(b) of thisform, the network of Figure 2 becomes amenable to computation whereby adesired impulse respense (curve 20 of Figure 4) may readily beaccurately matched. The reverse process is also computable, in that theimpulse response of a circuit of Figure 2 with a prescribed adjustmentof the sampling circuit-s 32, 33, 34, etc. 35, and 3601) or 36(11) maybe computed. Thus by employing network elements 21, 22, 23, etc. 24, 25(a) or 25(12) in Figure 2 which have impulse responses corresponding tothe Laguerre functions there is obtained a filter circuit completelyamenable to analysis by computation. The Laguerre coefiicients (an) arethe settings of the sampling circuits 32, 33, 34, etc. 35, and 36(a) or36(b). Therefore, by observing the optimum Iadjustments for thecalibrated sampling circuits 232-36 of Figure 2, the coefcients anbecome known. The operator will thus have the coeiiicients of theLaguerre series ywhich describes the impulse response of the optimumfilter system. Having also a lil-ter system adjusted for optimumfiltering the operator can observe its impulse response characteristic.In addition he can make a frequency response test and observe thefrequency response characteristic both as to phase and magnitude. Fromthese characteristics the operator may by means of standard techniquesdesign a circuit to match the characteristics which effect optimumfiltering. In this manner optimum adjustments in the impulsecharacteristic of the filter system can be made in the laboratory inorder to effect desired improvement in seismic response, and theseoptimum adjustments can be readily converted to a practical filter foruse in the field.

The adjustment of the sampling circuits 32-36 so as to edect the optimumsignal-to-noise ratio on the filtered seismogram requires a certaindegree of skill on the part of the operator butthe process can becarried out'by a systematic series of adjustments to the calibrateddials of the sampling circuits. The speed with which the proces-s iscarried out may be facilitated if the oper-ator will familiarize himselfwith the gener-al .fo-rm and behavior of the terms (ln) of the Laguerreseries previously mentioned. Familiarity Wit-h the envelope of theLaguerre coefficients (an fas a function of It) which result incommonly-used filter circuits will also be helpful. In addition, aknowledge of the transient response obtained from certain standardcombinations of sampling-circuit settings will be found helpful. As afurther aid the operator may employ charts showing the frequencyresponse obtained :from certain standard combinations of samplingcircuitsettings. With these various guidances the adjustment of the samplingcircuits to give the best possible filtering in any particular area maybe Iaccomplished by an experienced operator in a reasonable length oftime.

In the above-mentioned Ward publication it is shown that the frequencyresponses of Laguerre functions of the form l e-t-LDU), 11:0, 1, 2,Where Ln(t) is a Laguerre polynominal of degree n, are given by Where s-is the usual complex frequency variable and n is a positive integer.The circuit of Figure 5 can be connected in repeated cascade to form aladder network with this frequency response. An inductance 4,2" andresistor 7 43V areconnectedinseries across the input terminals 41. Inparallel with these is a condenser 44 and a resistor 45. Afl output"signal may -be taken either across resistor 45 as shown by terminals 47in which case the output-toe input frequency response ratio will be RCs/(l-l-RCS), or a'cross fthe resistor 43 as shown by terminals 46 in whichcase Ythe output-todnput frequency response ratio will beil/(.1f.I-.RCs.). If in the `circuit of Figure 5 the values of `theseparate resistors 43 `and e5 Vand the inductance 42 and the condenser44 are related by R2=L/ C then the Vcircuit will at all frequencies havean input impedance (as seen 'at yterminals 41) of pure resistance ofvalue R. It is .apparent that .instead of the resistor 45, one mayvagain substitute an entire network of the type shown in Figure. 5, 'andthis may in fact be done ad infinitum. Each' such Figure 5V section seesthe succeeding network asa pure resistance equal to R and so thefrequency response behavior through one section is unaffected by thepresence of other sections. Alternatively, instead of -resistor 43 onemay substitute a network of the type shown in Figure 5, and thissubstitution may be continued. In this manner it is possible to cascadeVsuccessive sections of the `general type of Figure to obtain a circuitwith the frequency response (RC's)m/(l-l-RCS)n where RC=L/R and m and nare positive integers. The sec'- ti'ons are `chosen to have impulseresponses corresponding 'to Laguerre functions and the impulse responseof a number of cascaded sections will correspond to a Laguerre function`of known form Kand degree. Continued subs'titution in successivesections respectively for resistor 43 or -resistor 45 (but always forthe same one) gives rise to ladder networks of the type employed in thisinvention and specific examples of which will now be described.

Figure 6 is a detailed wiring'diagram illustrating a circuitY networkthat forms one embodiment of this invention. The input terminals tl and5l are connected toi a `source of voltage which for test purposes may bean impulse generator previously described, or in service op-V erationmay be the voltage to be filtered. Output terminals 76 are 'connected.for test purposes to a cathode ray oscilloscope, or in serviceoperation to a recorder, amplifier 'and/or other devices in theelectrical channel. Connected between the input terminals 50 and 51 asshown in FigureV 6 is a series circuit comprising a condenser 52V inseries with a resistor 53. In parallel with this series circuit isa-.series circuit comprising an inductance '54 in series with a laddernetwork indicated genferally by 'the bracket 55, the latter comprisingthe condensers 556, 57, 58, etc. 59, inductances 6u, 6l, 62., etc. 63,and `resistors 64, 65, 66, etc. 67. A terminating Yresistor 68 isconnected across the end of the network. The condenser 52, resistor 53and inductance 5d, form the auxiliary network represented by 25fa) ofFigure 2. Themagnitudes of the various components of Figure 6 arerelated by the equation RzzL/C where R is the Vvalueof the resistance ineach branch, L is the value of the inductance in each branch, and C isthe value of the Vcapacitance in each branch. A branch is defined as 'asingle path between successive junction points. It is apparent that inthe circuit of Figure 6, each of the inductances, except inductance 5d,has a resistor connected in Series with it, whereby the losses (bothcore losses and'V copper losses) in the inductances can easily be .takeniinto account by Asimply reducing the `added resistance in the branch anequivalent amount. The frequency edect 4of internal resistance ininductance 54 can be compensated Jfor by a `shunt resistor of the propervalue across the inputterminals VVto sampling circuitv 7u. The various-components are connected as shown in Figure 6 and it is to beunderstood that the ladder portion indicated generally by bracket 55 maybe extended by the introduction of addit'ional Ysimilar sections. Inorder to attain good filter approximations one or two dozen suchsections .may be desirable. lIn the circuit'of Figure '6 the inputterminal network, so that thelead 69Tforms a running ground: This meansthat the various elements of the ladder sec7 tions are always operatedat the lowest practicall potential Vabove `ground whereby the effect ofdistributed capacity in these elements is minimized.

In Figure 6 the sampling circuits 71, 72, etc.V 73 and 74 are connectedto the ladder network so as to sample the voltage output of therespective ladder sections, and `the sampling circuit 70 is connected tosample the voltage output of the auxiliary circuit which precedes theladder network. It can be shown analytically that with an impulse inputthe signal vsampled by yeach of the sampling networks 70-74 correspondsto one of the Laguerre functions` of the form e-tLnO) where Ln() is theLaguerre polynomial of degree n'. The sampling circuits 7074havecalibrated adjustments so. that when the sampling circuits areadjusted the respective signal samples transferred willV be known bothas to polarity and relative magnitude. The sampling circuits 70-74 areconnected to `deliver their respective signals to a summing circuitwhich combines algebraically the respective sample signals- The combinedoutput is delivered at terminals 76( In the embodiment `of Figure 6 theinput terminal 51 may be grounded and the ground lead 69'forms a runningground connection that keeps one side of the ladder network at groundpotential. 'Furthermore one input terminal of each `of the Vsamplingcircuits 70, 71, 72, etc. 73, 74 :is thereby also maintained at groundpotential and -this further stabilizes the system. The ground connection69 is highly desirable in that it provides stability to the vacuurn-tubecircuits employed and it avoids unpredictable 'capacity and leakageeffects that accompany the use of iloating circuits. The calibratedsampling circuits 76-714 and the summing circuit 75 are well knownelements and will be described later.

p In Figure 6, the elements 52 and 53 are in parallel with the rest vofthe circuit comprising elements 54 and 55. It is apparent that theelements 52 and 53 have no effect on the voltages that are sampled bythe sampling circuits 7'3-74. 'Ihe elements 52 and 53 serve however tomake the network resistive as seen by the generator connected to theterminals 50 and 51. Accordingly if the particular generator that feedsinto terminals 50 and 51 does not require a purely resistive loadthenthe elements 52 and 53 may be omitted and such omission will have noeffect `on lthe output of the system as delivered to ter minals 76.

UFigure 7 shows a wiring diagram of another embodimentvof the inventioncomprising a ladder network indicated generally by bracket `87 followedby an auxiliary network similar to 25(12) of Figure 2. Terminals V80 and`81 are inputl terminals and oneV side of the input, as for 'exampleterminal fil, may be grounded. The ladder network comprises a condenser82 in series with an inductance 9i? and a resistor V94. Across theinductance 90 and resistor 94 is connected a' series circuit comprisingcondenser S3, inductance 91, and resistor 95. Across the Velements @land 95 there is again connected a condenser 84, inductance 92, andresistor 96. Additional sections may be added to the ladder in similarmanner as Vindicated by the dotted lines, andthe last section of theladder comprises condenser 85, inductance 93, and resistor 97. Thisladder network is followed by an auxiliary circuit comprising condenser-36 and resistor 93 connected across the inductance 93 and resistor 97of the last ladder section. The condensers S2, 83, 84, etc. 85 and 86all have equal capacity C, the inductances .90, 9i, 92, etc. 93 all haveequal inductance L, and the Vresistors 94, 95, 96, etc. Q7, and 93 allhave equal resistance R, the vvalues being given by the relation R2=L/C.

fThe embodiment of Figure 7 employs the auxiliary network following theladder and the auxiliary network also forms the termination for theladder $7. Sampling of each section is taken from across the resistorsuch as rSlt-isconnected to groundas -is also'oneside ofthe ladder 75`:94, l195,96, etc. 97 and these -voltages are Afed tothe 'calibratedsampling circuits 100, 101, 102, etc. 103. The sampling circuits provideknown adjustment of both magnitude and polarity of the sampled signal.The outputs of the sampling circuits are algebraically combined insumming circuit 105 whose output is delivered at output terminals 106.The ladder network of Figure 7 when terminated as shown gives a seriesof voltages `across the resistors 94, 95, 96, etc. 97 which correspondrespectively to Laguerre functions ofthe form e-t-LnU) where Ln(t) isthe Laguerre polynomial of degree n. Knowing the magnitude and sign ofeach of the sampling coecients (an) as determined by the setting of therespective sampling circuits, the circuit of Figure 7 is amenable tocomputation both as to transient response and as to equivalent filtercharacteristics. The circuit of Figure 7 is advantageous in that eachinductance is in series with a resistor, so that losses in theinductances may be accounted for in setting up the resistor of eachbranch to the proper value, namely, R2=L/C. This means that this circuitmay be set up to meet theoretical conditions to a high degree ofprecision. The fact that the samples are not taken across all of theequivalent resistance in the respective inductance plus resistancebranches is easily taken into account in Calibrating the `samplingcircuits t 100-103. The ground on terminal A81 also provides stabilityas previously mentioned.

Another circuit which may be employed in this invention is shown inFigure 8. This circuit is similar to that of Figure 7 except that it has`the condensers and inductances interchanged, and sampling is doneacross the condenser and resistor rather than across the resistor aloneas in Figure 7. The input terminals are 110 and 111 of which 111 maybergrounded. Each ladder section comprises an inductance such as 112 inseries with a condenser such as 120 and a resistor 124. Across thecondenser 120 and resistor 124 there is connected an inductance 1113 inseries With `a condenser 121 and resistor 125. Across the condenser 121and resistor 125 there isl again connected an inductance 114 in serieswith a condenser 122 and a resistor 126. This may be continued until thefinal section of the ladder is reached having inductance 115, condenser123, and resistor 127. This much of the circuit comprises the laddernetwork indicated by the bracket 117. The auxiliary network is connectedto follow the end of the ladder 117 and comprises inductance 116 andresistor 128. The auxiliary network also forms the termination. Theinductances 112, 113, 114, etc. 115 and 116 all have equal inductance L,the condensers 120, 121, 122, etc. 123 all have equal capacity C, andthe resistors 124, 125, 126, etc. 127 and 128 all have equal resistanceR, the values being given by the relation R2=L/ C. Samples from each ofthe ladder sections are taken from across the condenser and the resistoras shown in Figure 8 and fed respectively to the calibrated samplingcircuits 130, 131, 132, etc. 133. The sample voltages adjusted as toknown magnitude and polarity are algebraically combined by the summingcircuit 135 and the sum delivered to the output terminals 136. Thebehavior of this circuit can also be computed, but it does not meet therequirements of Laguerre functions, and the computations are much morelengthy and cumbersome because the functions describing the behavior ofthis circuit are not orthogonal as are the Laguerre functions. When thiscircuit is employed it is necessary to compute the coefficients (an)from a set of simultaneous equations involving the settings of thesampling circuits 130-133. Accordingly this circuit is not asadvantageous as those of Figures 6 or 7. However, the circuit of Figure8 has a running ground (from terminal 111) in the manner similar toFigures 6 and 7.

A still further embodiment of this invention is illustrated in Figure9.' The network of Figure 9 shows a different type of ladder than thepreviously-described embodiments in that it comprises a series of vacuumtubes indicated by the bracket 147. The ladder is preceded by anAauxiliary networkcomprising inductance 142 and reif sistor 143 connectedas shown to input terminals 140 and 141 of which 141 may be grounded.Inasmuch as the succeeding sections of the ladder network 147 areentirely' similar only one of them will be described. Eachsectioncomprises a vacuum tube 144 which is indicated as a triode butother multi-element tubes connected for triode` operation may beemployed. By way of example, one: unit of a Itype 12AU7 tube has beenfound satisfactory as@ tube 144. The input of the section is connectedto the grid of tube 144. The plate circuit of the tube comprisesresistor 145 and the cathode circuit comprises resistor 146. Platevoltage supply is connected as indicated at the B+ terminals. The anode(plate) resistor 145 is made: equal to the cathode resistor 146 in each.section, but their value need not necessarily be the same as that ofsimilar resistors in each of the other ladder sections. By way ofexample, resistors 145 and 146 may each be 1000 ohms. A series circuitcomprising condenser 148 and resistor 149 is connected from the plate tothe cathode of tube 144. Output signal of each section is taken from thejunction between condenser 148 and resistor 149. The value of thecondenser and resistor is chosen so that for all sections the productRC=constant, where R is the resistance of resistor 149 and C is thecapacity of con denser 148. It is not necessary that the resistors 149be the `saine in all sections or that the condensers 148 be the same inall sections, provided only that their product RC is the same for allsections. By way of example, a capacity of 0.005 mfd. for condenser 143and a resistance of 1 megohm for resistor 149 have been foundsatisfactory for operations with seismic signals. 'Ihe value of theinductance 142 and the resistor 143 of the auxiliary circuit are suchthat L/R=RC=constant. A sample voltage is taken from across the resistor143 of the auxiliary network and fed to the calibrated sampling circuit150. Voltage is sampled from each section of the ladder network from thejunction between the condenser 148 and the resistor 149 as shown inFigure 9 by calibrated sampling circuits 151, 152, etc. 153. The sampledsignals are adjusted in polarity and amplitude by kn-own amounts in thecalibrated sampling circuits. The outputs of all of the samplingcircuits 150-153 are combined algebraically by summing circuit anddelivered at terminals 156.

In the above-mentioned Ward publication it is shown that the frequencyresponses of Laguerre functions of the form et-Ln(2t), n=0, 1, 2, WhereLn(2t) is a Laguerre polynomial of degree n, are given by where s is theusual complex frequency variable and n is a positive integer. Ward aswell as Aigrain and Williams (ref. cit.) point out the computationaladvantages of this form of Laguerre functions. The frequency response ofthe tube circuit comprising elements 144, 145, 146, 148, and 149 ofFigure 9 is (l-RCs)/(l|-RCS). In this invention a series of such tubecircuits are cascaded in a ladder network with the proper initialsection in order to obtain the desired Laguerre function impulseresponse. The circuit of Figure 9 is advantageous in that it has but oneinductance. A-n amplifier such as 160, 161, etc. is connected ineachladder section in order to supply energy and make up for attenuation inthe tube 144 of the section. The amplifiers 160, 161, etc. areconventional singlestage repeater circuits and are shown onlyschematically in Figure 9 and will be described in detail later. Theampliiiers are tied into the running ground 141 and also provide intheir output circuit means for tieing down the grid of the succeedingtube as will become evident later in the detailed explanation of Figure17. The adjustment of ampliers 160, 161, etc. will be explained later.

Figure l0 shows another embodiment of this invention in which atube-type ladder network 167 is employed. Input terminals are 170 and171.0f which 171 may be grounded. The auxiliary circuit compriseslresistor 172 andlcondenser 1:73. The voltage across the condenser-173is: sampled by calibrated sampling circuit 180. The tube-v type laddernetwork 167 employingrtriode tubes such as 174 is in all Vrespectssimilar to that of 1-47 of Figure 9; In Figure 10 the anode resistor 175of tube 174 is made equal to the cathode resistor 176 in each section,but their value need not necessarily ybe the same as that of similarresistors in each of the other ladder sections. The product ofthecapacity (C) of condenser 178 and the resistance (R) of resistor 179 isthe same for each section and alsorequal to the product RC for resistor172 and condenser 173 of the auxiliary network. Sample voltages aretaken from the various sections of the ladder 167 by means of calibratedsampling circuits 181, 182, etc. 183.V The outputs of the samplingcircuits 180-183 are adjusted as to known amplitude and known polarityand are algebraically combined by summing circuit 185 and delivered tothe output terminals at 186. The impulse responses of the circuit ofFigure l at the sampling points can also be shown to correspond toLaguerre functions of the form et-Ln(2t), where Ln(2t) is a Laguerrepolynomial of degree n. The circuit is particularly advantageous in thatno inductances are employed. Condensers can usually be made highlyeicient so that it is possible with the circuit of Figure 1 0 to set upthe theoretically-required conditions to a high degree of precision.Inasmuch as terminal 171 is grounded, each section of theiladder as wellas the sampling circuits are provided with a high degree ,of stability.lIn order to compensate for attenuation in the tubes 174 of the laddernetwork ampliiers such as 187, 188, etc. are included in each laddersections in a manner similar to Figure 9. 'Ihe gain of amplitiers1187,'18, etc. is adjusted to provide the proper compensation as will bedescribed.

t In the embodiment of Figure the grid potential of tube 174 must betied down through the input circuit connected to input terminals 170 and17.1. A high grid leak resistance may be connected in parallel withcondenser 173.. The values of the grid leak resistor, resistor 172 andcondenser 173 must be such that the parallel combination of the tworesistors and the condenser must have the same RC product as condenser17S and resistor 179. lSome attenuation does occur in this circuit.

A preferred embodiment of the invention is shown in Figure l'l, in whichthe ladder network 247 is in all respects similar to the ladder networkA147 and 16.7 of Figures 9 and .10. The auxiliary `circuit whichprecedes the ladder network 247 comprises an integrator 254 connected tothe input terminals 240 and 241 of which the latter may be grounded asshown. The integrator 254 is conventional and will be described indetail later. In series with the integrator is a condenser 242 having acapacity (C) and a resistor 245 having a resistance (R) connected asshown. The circuit comprising theintegrator 254, condenser 242 andresistor V2,43 ,can be shown to vproduce across resistor 243 an impulseresponse that corresponds to a Laguerre function of the form whereL0(2t) is the Laguerre polynomial of degree zero. The ladder network 247is connected across the resistor 243 as shown. Each, section of theladder comprises a tube 244 having cathode resistor 246 and anoderesistor 245. The anode resistor 245 is made equal to the cathoderesistor 24e, but their value need not necessarily be the same as thatof similar resistors in each of the other .ladder sections, VFrom anodeto cathode there is connected a series circuit comprising condenser 248and resistor 249. The vproduct of the capacity (C) of condenser 24,8 andthe resistance (VR) of resistor 249 is the -same for each ladder sectionand is also equal to the RC product for condenser ,242 and resistor'243. The junction between condenser 1248 and resistor 249 is connectedtoenamplier whose gairrs adjusted to corn- I2 pensate for. attenuationin the circuit of ltube 244.as.will be described. It can be shown thatthe circuit of- Eig: ure. 1l willY produce at the end of each laddersection (comprising the circuit of a tube' 244 and'an amplifier 264i).an impulse` response that corresponds to'a Laguerre function of theforme-t-Lnr) where L(2t)` is the Laguerre polynomial of degree n. ThevoltageV across resistor 243 of the auxiliary circuit is sampled by thecalibrated sampling circuit 2519, and the output voltages of therespective ladder sections are sampled by 'the calibrated samplingcircuits 251, 252, etc. 25,3. The outputs of the sampling circuits areadjusted as to known arnplitude and known polarity with respect to theirre; spective input signals and. algebraically combined by summingcircuit 255 and delivered to the Voutpiit'te'rminals 256. It is seenthat the circuit of Figure l1 has a running ground which provides thenecessary stability, it employs no inductances whereby very highprecision can be attained, and the grid of tube 244 is provided with agrid resistor. The resistors 246 and 249 togetherform the grid resistorfor the tube in the succeeding amplifier 260 as will become evidentlater. The circuit of Figure ll is the preferred embodiment of theinvention.

Figure 1l has a further practical advantage. TheV impulse response ofthe networks of lthis invention'is termined by applying to the inputterminals in each case a signal like'that of Figure 3. Howeverin thecase of Figure ll, the' same result can alternatively lbe obtained byapplying to terminal 257 a wellknown step function input. No specialapparatus is required to produce a step function input and thissimplifies thistest when using the circuit of Figure ll. Y

Figures l2 and 13 show examples of sampling circuits which may beemployed with any of the embodiments of this invention. The samplingcircuits are known and do not per se form the subject matter o f thisinvention. inasmuch as one terminal of each ladder section and also ofeach auxiliaryV circuit is grounded, the sample voltage is in eachinstance taken with respect to this, ground. It is accordingly highlydesirable to maintain a ground in thel sampling circuits.

In the sampling circuit of Figure l2 the voltage to be sampled isapplied at terminals 190 one or" which is grounded as shown at 189. Thesample voltage is passed through a transformer 191 which preferably isof a type having high delity at the frequencies of interest intheparticular problem being studied. For example, in the case of seismicoperations the frequency response of the transformer 191 should besubstantially iiat from about 3 to about 30() c.p.s. The secondary oftransformer 191 is connected to a reversing switch 192 and to the endsof a calibrated potentiometer 193. By means of the potentiometer slider194 any known fraction of the transformer secondary voltage may betapped o and its po larity may be made to have the desired Avalue byappropriate manipulation of the reversing switch 192. vThe potentiometerslider 194 is calibrated to show the fraction of the voltage atterminals 1% that is delivered at terminals 1195. The impedance of thecircuit of Figure 12 as seen at terminals 190 should lbe high comparedto that of the network to which it is connected. M"'lihevadjusted samplevoltage is delivered at terminals 195V and it 1s apparent thatone ofthese terminals may be ,grounded if desired.

Figure 13 shows another known type of sampling circuit which employs avacuum tube 196. The input, i.e., the signal to be sampled, is appliedat terminals 197,'o'ne of which may be grounded `as shown at 206mFigurelS. The ungrounded terminal is connected tofthe grid of tube 196and to a :grid resistorr19. The resistance of grid resistor 198 shouldbe high compared tothe impedance of the network yto which the Yinputterminals -197 arerconnected and may be ofthe orderof l megohm.Therlcathode .of tube 19d-has a` resistor 199 and the anode hasaresistor N0-whose resistance-Value-is the same'asr resistor V199.Resistors 199 and 1200 may lr'or example each have a resistance of 5000ohms. Plate voltage is supplied at the terminal marked B+. The output oftube 1.96 may .be taken -either from the cathode or the anode. Tube 196may be a .triode as rfor example one unit of a type 12AU7 tube or may besome other type in which an equivalent triode connection is employed.Inasmuch as the same tube current flows through resistor 199 as flowsthrough resistor 200, the output may be taken either from the cathode orthe :anode and these two voltages diter only in sign. Accordingly, asinglepole `doublethrow switch 201 is provided so that the samplevoltage may be made to have the desired polarity. A decoupling networkcomprising condenser 202 and potentiometer 203 is connected `as showninl order to isolate the output terminal 204. The ydecoupling networkmust not attenuate vfrequencies .of interest and, `for example,condenser 202 may have a capacity of 2 mid. and potentiometer 203 mayhave a resistance of 1 megohm. The circuit of Figure 13 may be made tooperate at frequencies .as low as desired .by proper Idesign of the timeconstant attained by condenser 202 and potentiometer 203. It is apparentthat in the circuit of Figure 13 one of the output terminals 204 isnecessarily grounded. The magnitude of the output voltage delivered atterminals 204 is determined by the adjustment of the potentiometerslider 205 and its polarity is determined by the setting of the switch201.

In cali-brating the sampling circuit of either Figure 1-2 or Figure 13,.the potentiometer slider (194 or 205 respectively) is calibrated inconjunction with the rest of the respective sampling circuit to indicatethe fraction of the voltage at terminals 190 or .197' respectively thatis delivered by the sampling circuit to terminals .195 or 204respectively. It is essential that all of .the sampling circuitsconnected to the particular network employed be accurately calibratedwith respect to each other. Such calibration may easily be made lbyapplying a steady A.C. signal of vfrequency with the range offrequencies of interest to the separate sampling circuits and employinga vacuum tube voltmeter to compare the input and output voltages atvarious settings of the potentiometer (194 or '205) in well-knownmanner.

The circuit/employed for algebraically combining the outputs .of thesampling circuits will depend on the type of sampling circuits employed.It is apparent that if the sampling circuit of Figure -12 is used, andno ground is placed on the secondary of transformer 191, the combinationof outputs of such circuits may be obtained by simply connecting theoutput terminals 195 (Figure 12) in series. Figure 14 shows such acircuit in which the various adjusted sample voltages (obtained from thesampling circuits such as Figure 12) are applied to terminals 225, 226,227, etc. 228. The individual voltages are summed algebraically by theseries circuit and .the sum is delivered to output terminals 230. -Onthe other hand if the sampling circuit of Figure 13 is employed, theoutput circuits may -be connected in parallel as shown in Figure 15. InFigure 15 .the terminals 210, 211, 212, etc. -213 are connected to .theoutput of the respective sampling circuits i.e., terminals 204 of Figure13. One of each ot the terminals 210-213 may 4be grounded as shown `at214, and of course this corresponds to the grounded terminal (206) ofthe respective pairs 204 of Figure 13. Each of the other terminals isconnected to a separate high impedance load resistor 215, 216, 217, etc.218. The other terminals of the resistors 215-218 are connected to acommon lead 220 which is connected through a common resistor 221 toground. The resistors 21S-218 are made to have a high impedance withrespect to the resistor 221 (as well as with respect to potentiometer203 of Figure 13) and the resistors 215418 are all made equal. By way ofexample, the resistors 21S-218 may each have a resistance of 1 megohm orhigher, whereas the resistance of resistor 221 may be in 14 `the orderof1000 ohms. It is apparent that the current in resistor 221 is .the sumof the currents in resistors 21S-218, and sinceresistors 21S-218 are allequal, the v potential across resistor 221 will he proportional to thesum of .the voltages applied to the .terminals 210-213- This voltage maybe amplified by means ot an amplifier 222 and delivered to the outputterminals 223. The gain of amplier 222 is adjusted to compensate for theattenuation that results trom the series connection of resistors 21S-218respectively yand the resistor 221.. By way of example if resistors21S-218 are 1 megohm and resistor 221 is 1000 ohms, then the gain ofamplifier 222 should be 1000. The system including amplifier 222 iscalibrated so that the voltage delivered at terminals 223 will be theal-gebraic sum of the voltages delivered to the terminals 210-213. i

Figure 16 shows a vwiring diagram of the integrator 254 of Figure 11.The integrator of Figure 16 is well known in the art. 'I'he inputterminals of the integrator are 270 and `271, which correspond toterminals 240 and 241 respectively of Figure 11. The output terminals ofthe integrator are 280 and 281 which correspond to terminals 257 `andv241 respectively of Figure 11. Terminals .271 and 281 may be groundedand this conforms to the running ground 241 of Figure 11. A resistor 272is connected in series with a condenser 273 between input terminal 270and output terminal 200. The condenser 273 `is bridged by adirect-current amplifier 274, one side of which may be grounded. It canbe shown that the circuit of Figure 16 ydelivers at terminals 280-281 asignal that is the time integral of the signal applied to .terminals270-271. In order to achieve fidelity in the integration the timeconstant (RC) of the combination of resistor 272 and condenser 273multiplied by the amplijier .gain should be large compared to the periodof the longest frequencies of interest. By way of example, values of lmegohm and 0.01 mfd. respectively have been found adequate foroperations on seismic impulses. The gain of lampliler 274- is notcritical and may yfor example be in the neighborhood of 30,000.

Figure 17 shows a detailed Wiring diagram of an ampliier which may beemployed in any of the embodiments of Figures 9, 10, or 11 as theelement indicated by 160, 161, 187, 1818, 260, or 261. The amplifiercomprises an amplifying device such as -tube 283 which may be a triode,as for example one unit of a type 12AU7 tube. One input terminal 285 andone output terminal 291.0f the amplifier may be grounded as shown.VInasmuch as this ground is conventional it is not shown on the Figures9, 10, and 1l. The other input terminal 284 is connected to the grid oftube 283. The grid potential is tied down by the resistors in thepreceding tube se@ tion, namely 146 and 149 of Figure 9, 176 and 179 ofFigure 10, 246 and 249 of Figure 11. A cathode resistor 287 connects thecathode of tube 283 to ground. The resistance of resistor 287 may be ofthe same order as thecathode resistor in the preceding tube stage. Avalue of 3300 ohms for the resistor 287 has been found adequate. Theplate ofA tube 283` is connected to the B-voltage supply through plateresistor 286 Whose value is made much larger than the resistance ofresistor 287 and which is preferably made adjustable. A value of about7000 ohms for resistor 286 has been found satis'- factory. The amplifiedsignal is transmitted to the grid of the tube in the succeeding laddersection through a decoupling network comprising a condenser 238 havingcapacity (C) in series with a resistor 289 having resistance (R)connected from the plate of tube 283 to ground. The CR product forcondenser 288 and resistor 289 is made very large compared to the CRproduct for condenser and resistor in the preceding tube circuit, i.e.large compared to CR for elements 148 and 149 of Figure 9, elements 178and 179 of Figure 10, and elements 248 and 249 of Figure l1.

Inasmuch as the circuit of Figi ure 17 must be capable of good frequencyresponse to Very low frequencies Vi.e,.lower than the lowest frequencyof interestin the signal to be analyzed, it is preferred that the CRproduct be yery large. A capacity of Z'mfd. for thecondenser 288 and avresistance of 5V megohm for the resistor289 has been found satisfactoryfor operations in seismic frequency ofrange. i The values given for, thevarious components of Figure 17 are by way'of example only, nand thesewi1l` result in an amplifier havingv Substantially liat response down toa frequency'of about 1 cps'. i

In each of the circuits Figures 9, and l-1 it will be apparent vthat acertain amount of attenuation will occur inthe tubes 144, 174, 0h24@respectively'iand the purpose ofthe immediately-succeeding amplifiers160, 187, orV 266 respectively, which may be ofthe form shown in Figure17A, is to restore the signal to its original amplitude. Accordingly theamplificatic'mV of the respective amplifiers 16o, 161, 1.187, `188,260,261, etc.A isadjusted to provide Vin. each ladder section the properamplification.i The amplification of the amplifier of Figure 17 may beadjusted in any one of a variety of 'conventional ways', as forV exampleby adjustment of theplate resistor 286; y inasmuch as thetubes 14?.,174, and 244 may vary slightly in .the respective Sect-ions of theladder networks, each'ladder section is adjusted individually. The .gainof the amplifier is'adjustedso that .there is no net attenuation throughthe section, ile. so that the voltage output of the amplifier 160 forexample is the Same as the voltage input to the grid of the precedingtube 1444K These adjustments may be rn'ade'by applying a steady A.C.signalbf frequency within the range of frequencies of interest to theinput of the respective ladder sections'and adjusting the gain of eachamplifier (eg. by adjusting resistor 2 86 of Figure 17) so that theoutput of the section is equal to the input as' measured with aVacuumtube voltmeter. Best precision is attained 'if this adjustment ismade without disconnecting the respectiveY la'd'der sections or therespective sampling circuits whichl load the amplifier slightly andltherefore may affect it'sgain.

By using the filter networks 'of thisinventionfthe coeliicients' (an) ofa Laguerre series characterizing the filter are read off the calibratedadjustments of the sarnpling networks directly. It is to be vnoted thatthe Laguerre vseries for the'V circuits of Figures`6 and 7 differ fromthat of Figures 9 l0, and 11. lvEachhofwever'has certain advantages.Figures 6 and 7 have aminjmum of vacuum tubes whichV may be an advantagein certain applications. On the other hand Figures 9*, v 10,Y andv 11have the advantage of greater'computationalflexibility and permit theintroduction of amplifiers to'compensate attenuation down the extendedladdernetWOIkv so vthat a greater number of sections may be usedV withcorresponding increase in precision. The circuits of this'invefntion, bydirectly indicating the Laguerre coe'flcients, permit the operator toquickly arrive at the characteristies'of an optimum filter for recordingtransient'phenornena when accompanied by noiseor other extraneousyvibrations.

In the'circuits of Figures 9, 10, and llthe'condensers 14S, 178, 243respectively land the resistors149,179,V 249 respectively may beinterchanged and this results merely in changing the sign of theLaguerre Vterms ofodd degree (Le. those forY which n is odd) inVtheLague'rre series characterizing the filter. It is apparent, however,that s uch an interchange in the circuit `will require that means beprovided for blocking plate voltage of tubes 144, 174, 244 respectivelyfrom the grid of the next tube ile. the tube of amplifiers 161i, 187,260respectively, and will ,also require means for ticing down the gridl ofthe next tube. 'V

While the filter circuits of this invention have been described withparticular reference to seismic recOrding, this is merely by way ofexample and Qtlieruses will be evident torthose skilled inthe art.Furthermore, Whereas the described purpose of the filter 'of thisinvenlion fis -to' obtain the Laguerre coeiiicients [of an optimum namedlbrarwlhes whereby 'the instantaneous i/Qlt filter so that furtheranalyses and computations can readil'y be inade, vit` is apparent thatifV desired the circuits herein disclosed and claimed may beemployedasadj table filters without necessarily 'using the`Lagu`errecoefiicients so obtained. Y

` What I claim as my invention'is: l

l. An adjustable electrical filter circuit comprising a pair of inputterminals, a'series branch consisting ofv two equal inductances L andresistance R connected between said input terminals, a Vplurality'ofcircuit branches eaeli consisting of capacitance C and inductance L andVresist-` ance'R in series, saidcircuit branches being connectediincascade so that the vfirst branch is connectedl in" parallel with one ofsaid firstnamed inductances and saidirsrnamed resistance, and eachVsucceeding `branch connected in parallel with the inductance andresistance of the precedingbranch, a circuit branch cvzonsisting "of a'capacitance `C and resistance R inseries connectedi' parallel with theinductance andi resistance of thelast of said cascaded branches, wherebyeach of said resistance's has acommonterminal con'nectedto one ofsaidinputV terminals, the magnitude or" earch of said inductances'L'aId," capacitances 'C and resistance 1R being related 'by the "ejpressiori R2=L/C, a plurality of electrical connections leading toseparate respective junctionsof said branches with' a' preceding branch'whereby the instantaneoll V911: ages at said'junctions may be sampled, aplurality` df voltage-adjusting means connected to said connectionsrespec'tively developing instantaneous voltages.` related' tp saidvoltagesirl known polarity and known amplitud'ejand means connected to aplurality of said voltage-adjusting means algebraically summing thesignals thereof, 2. An adjustable electriciilter circuit comprising apair of input terminals', a plurality of circuit branches' f consistingof a capacitance C and inductance L and 'resi ance R- connected inseries, said circuit branches Vbeing connected incascadeso that thefirst branch'is con ,l ed to said'input terminals 'andV each succeedingbranch' is 'c o nected in parallel with the inductanceand resistanceofthe preceding branch, a terminating branch consisting of :acapacitance 4C and a resistance R in series' connected; in parallel-withthe inductance and resistance offthe'fla'st of said cascaded branches,whereby each of said resistancs has acommon terminal connected to one ofsaid Vin ut terminals, the magnitude of each of said induct` L4 andcapacitances Cand resistances R being relatedby expression R2='L/C, aplurality of electrical" co'nnecV leadingto terminals of respectiveresistances in 'saidv across said resistances may be sampled, a pluralitvoltage-adjusting means connected'ftQ Said' connee spectively developingvinstantaneous voltages said voltages in known polarity' and known amplid means connected to a 'plurality'of said voltagemeans algebraicallysumming the signals thereof;

3. An adjustable electric'filter'circuitcomprising a pair of inputterminals, a plurality of circuit b, ,Y 'ac' consisting of aninductance`L and 'capacitance"C- resistance R connectedinseries, "saidcircuitbranches being connected in cascade so that the lirst' branch islcn-l nected to said input terminals and each succeedirig b` isconnected in parallel with the capacitance and r nected in parallel withthe capacitance and resistance "of, the last of said cascaded branches,`whereby a'chlb'ffsaid resistances has` a 'common'term-inal connectedtofonef. said 'input terminals; me' magnitude or senor 'seid i ductancesL and Acapacitances C and\resista'rices` R'be' related by the expressionR2=L/C, a pluralityV fel` cal connections leading to separate respectivejunction if saidbraiiches with a'pre'ceding branch; anelitoV the ofsaid: terminating branch 'with its prec y r, whereby the instantaneousvoltages at said junctions may aJ-apled, a plurality ofvcltage-adjustingmea'ns' c'nnected to said connections respectivelydeveloping instantaneous voltages related to said voltages in knownpolarity and known amplitude, and means connected to a plurality of saidVoltage-adjusting means algebraically summing the signals thereof.

4. An adjustable electric lter circuit comprising a pair of inputterminals, a ground connection to one of said input terminals, aninductance L and a resistor R connected in series from said ungroundedinput terminal to said grounded input terminal, an electrical connectionto Ithe junction of said resistor and said inductance, a plurality ofvacuum-tube circuits each consisting of a vacuum tube having a grid andanode and cathode, a cathode resistor connecting said cathode to saidground connection, an anode resistor connected to said anode, saidcathode resistor and said anode resistor having equal resistance, acondenser C and a resistor R connected in series from said anode to saidcathode, the magnitude of each of said inductances L and said resistorsR and said condensers `C being related by the expression L/R=CR=constant, an electrical connection to the junction of said condenser Cand said resistor R, the rst oi said vacuum-tube circuits having itsgrid connected to the junction of said first-named inductance L andresistance R, means connecting the grid of each of the other of saidvacuum-tube circuits in cascade to the junction of said last-namedcondenser vC and resistor R of the preceding circuit, a plurality ofelectrical connections leading respectively to the junctions of saidlast-named condenser C and resistor R of said vacuum-tube circuits, aplurality of voltage-adjusting means connected to said connectionsrespectively developing voltages related to said voltages in knownpolarity and known amplitude, and means connected to a plurality of saidvoltage-adjusting means algebraically summing the signals thereof.

5. An adjustable electric filter circuit comprising a pair of inputterminals, a ground connection to one of said input terminals, aresistor R and a condenser C connected in series from said ungroundedinput terminal to said grounded input terminal, an electrical connectionto the junction o-f said resistor and said condenser, a plurality ofvacuum-tube circuits each consisting of a vacuum tube having a grid andanode and cathode, a cathode resistor connecting said cathode to saidground connection, an anode resistor connected to said anode, saidcathode resistor and said anode resistor having equal resistance, acondenser C Vand -a resistor R connected in series from said anode tosaid cathode, the magnitude of each of said condensers C and saidresistors R being related by the expression CR=constant, an electricalconnection to the junction of said condenser C and said resistor R, theAfirst of said vacuum-tube circuits having its grid connected to thejunction of said first-named resistor R and condenser C, meansconnecting the grid of each of the other of said vacuum tube circuits incascade to the junction of said last-named condenser C and resistor R ofthe preceding circuit, a plurality of electrical connections leadingrespectively to the junc- -tion of said last-named condenser C andresistor R of said vacuum-tube circuits, a plurality ofvoltage-adjusting means connected to said connections respectivelydeveloping voltages related to said voltages in known polarity andyknown amplitude, and means connected to a plurality of saidvoltage-adjusting means algebraically summing the signals thereof.

6. An adjustable electric iilter circuit comprising a pair of inputterminals, a ground connection to one of said input terminals, anelectric signal integrator connected to said input terminals and havingone ungrounded output terminal, a condenser C and a resistor R connectedin series `from the ungrounded output terminal of said integrator toground, an electrical. connection to the junction of said resistor andcondenser, a plurality of vacuum-tube circuits each consisting of avacuum tube having a grid and anode and cathode, a cathode resistorconnecting said cathode to said ground connection, an anode resistorconnected to said anode, said cathode resistor and said anode resistorhaving equal resistance, a condenser C 'and a resistor R connected inseries from said anode to said cathode, the magnitude of each of saidcondensers C and said resistors R being related by the expressionRC=constant, an electrical connection to the junction of said condenserC and said resistor R, the iirst of said vacuum-tube circuits having itsgrid connected to the junction of said first-named condenser C andresistor R, means connecting the grid of each of the other of saidvacuum-tube circuits in cascade to the junction of the last-namedcondenser C and resistor R of the preceding circuit, a plurality ofelectrical connections leading respectively to the junction of saidlast-named condenser C and resistor R of said Vacuum-tube circuits,whereby the instantaneous voltage at said junctions may be sampled, aplurality of voltageadjusting means connected to said connectionsrespectively developing Voltages related to said voltages in knownpolarity and known amplitude, and means connected to a plurality of saidvoltage-adjusting means algebraically summing the signals thereof.

References Cited in the le of this patent UNITED STATES PATENT-S2,263,376 Blumlein et al. Nov. 18, 1941 2,790,956 Ketchledge Apr. 30,1957 2,823,303 McCoy Feb. 11, 1958

